Extended balancing of continuous LTI systems: a structure-preserving approach

TL;DR

This paper develops a structure-preserving extended balancing method for continuous-time LTI systems, specifically targeting port-Hamiltonian systems, to achieve reduced models that maintain physical interpretability and have bounded errors.

Contribution

It introduces conditions for structure-preserving model reduction using extended Gramians in port-Hamiltonian systems, enhancing physical interpretability and error bounds.

Findings

Conditions for structure preservation established

Extended Gramians enable small error bounds

Reduced models retain physical interpretation

Abstract

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model.